Analysis of dynamic failure of the discrete chain structure with non‐local interactions

Gorbushin, Nikolai; Mishuris, Gennady

doi:10.1002/mma.4178

Cited by 17 publications

(25 citation statements)

References 34 publications

(96 reference statements)

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“…The analysis of this energy release rate ratio was also carried out for a triangular cell lattice by Fineberg and Marder (1999) and Marder and Gross (1995), for a chain with anisotropic properties (see Gorbushin and Mishuris (2018)) and non-local interactions (see Gorbushin and Mishuris (2016)). We note that the expression in (80) is also valid for the Mode III crack propagating in dissimilar media and this is derived in the Supplementary Material SM.8.…”

Section: Dynamic Features Accompanying the Fracture Processmentioning

confidence: 99%

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Dynamic phenomena and crack propagation in dissimilar elastic lattices

Gorbushin

Mishuris

Movchan

2020

International Journal of Engineering Science

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Dynamic Mode III interfacial fracture in a dissimilar square-cell lattice, composed of two contrasting mass-spring lattice half-planes joined at an interface, is considered. The fracture, driven by a remotely applied load, is assumed to propagate at a constant speed along the interface. The choice of the load allows the solution of the problem to be matched with the crack tip field for a Mode III interfacial crack propagating between two dissimilar continuous elastic materials. The lattice problem is reduced to a system of functional equations of the Wiener-Hopf type through the Fourier transform. The derived solution of the system fully characterises the process. We demonstrate the existence of trapped vibration modes that propagate ahead of the crack along the interface during the failure process. In addition, we show as the crack propagates several preferential directions for wave radiation can emerge in the structured medium that are determined by the lattice dissimilarity. The energy attributed to the wave radiation as a result of the fracture process is studied and admissible fracture regimes supported by the structure are identified. The results are illustrated by numerical examples that demonstrate the influence of the dissimilarity of the lattice on the existence of the steady failure modes and the lattice dynamics.

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Section: Dynamic Features Accompanying the Fracture Processmentioning

confidence: 99%

“…Different intermolecular interactions in a discrete system also affect phase transitions. We refer to the work of Gorbushin and Mishuris (2016), where admissible failure regimes in chains with non-local interactions were studied. Slepyan (2005) considered the influence of distributed mass along the lattice connections on lattice fracture.…”

Section: Introductionmentioning

confidence: 99%

Dynamic phenomena and crack propagation in dissimilar elastic lattices

Gorbushin

Mishuris

Movchan

2020

International Journal of Engineering Science

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“…Here, we give the representation of the envelope functions for the reflected and transmitted waves encountered during the failure process based on (28) and (29). The expressions for the associated waveforms in the structure may then be determined by combining the results presented here with (11).…”

Section: Dynamic Features For the Alternating Generalised Strain Regimementioning

confidence: 99%

“…In Figures 10(a) and 10(b), we compare the MATLAB simulation data for the arrangement of the masses along the profiles with the analytical results of Section 4 and [45,46]. In Figure 10(a), for the computations based on the analytical results, the inverse Fourier transform of (28) and (29) is computed using (39), ensuring that (33) holds for the feeding wave phase determined from (32). For the computations in Figure 10(b), the same procedure is followed based on the results of [45,46].…”

Section: Behaviour Of the System During The Dynamic Failure Processesmentioning

confidence: 99%

“…Failure regimes in discrete structures with non-local interactions and their effects on the wave radiation processes are presented in [28] and for media with additional non-linearities in the connections see [29]. Macro and micro-level models for the reversible decohesion of finite elastic layers, associated with the denaturation of DNA, are considered in [30].…”

Section: Introductionmentioning

confidence: 99%

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Alternating Strain Regimes for Failure Propagation in Flexural Systems

Garau

Movchan

Jones

2019

The Quarterly Journal of Mechanics and Applied Mathematics

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We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler-Bernoulli beams. A fault inside the structure is assumed to propagate with a constant speed and this occurs as a result of the action of a remote sinusoidal, mechanical load. The established regime of fracture corresponds to the case of an alternating generalised strain regime. The model is reduced to a Wiener-Hopf equation and its solution is presented. We determine the minimum feeding wave energy required for the steady-state fracture process to occur. In addition, we identify the dynamic features of the structure during the steady-state fracture regime. A transient analysis of this problem is also presented, where the existence of steady-state fracture regimes, revealed by the analytical model, are verified and the associated transient features of this process are discussed.

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On weak solutions of boundary value problems within the surface elasticity of Nth order

2021

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A study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining the weak solution. In order to characterize the smoothness of such solutions, certain energy functional spaces of Sobolev type are introduced. Compared with the solutions obtained in classical linear elasticity, weak solutions for solids with surface stresses are smoother on the boundary; more precisely, a weak solution belongs to H1false(Vfalse)∩HNfalse(Ssfalse) where Ss⊂S≡∂V and V⊂double-struckR3.

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Analysis of dynamic failure of the discrete chain structure with non‐local interactions

Cited by 17 publications

References 34 publications

Dynamic phenomena and crack propagation in dissimilar elastic lattices

Dynamic phenomena and crack propagation in dissimilar elastic lattices

Alternating Strain Regimes for Failure Propagation in Flexural Systems

On weak solutions of boundary value problems within the surface elasticity of Nth order

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